I have driven more times than I care to count from extreme northern Maryland (near Hanover, PA). Being an over ambitious planner, I keep track of every drive in a spreadsheet. We average 14.5 hours of actual driving time and about 2.5 hours of breaks. We always try to leave at a time that will put us driving through the DC/Northern Virginia area between 10pm and 5am (if travelling on weekdays) because the time from DC beltway to North Carolina can easily range from 2.5 hours to 5.5 hours of pain.
After a good 20 years of data collection, the past few trips we have done about the same plan. Leave our home on Saturday early afternoon and arrive on Sunday morning for park opening at one of the parks. My wife and I trade off driving every 3 hours or so and sleep while the other drives. We take about half an hour for dinner and then usually stop for an hour twice in rest areas in the middle of the night and we all sleep for a little bit.
We have done the trip over two days before and gotten a hotel for the night, but we actually find that our car is more restful than a cheap hotel (and certainly even cheaper). Our total trip cost each way is about $150 (gas, a meal, and snacks) while airfare for the 3 of us is close to $600 total, so we save about $300 which buys a lot of Dole Whips.
It does make the first day a little exhausting in the parks, but our usual plan is to get into a park at opening, then get out around lunch, head to our resort (praying that our room is ready) and then rest for a few hours (either in room or by the pool). By that evening we are back on track and ready to go!
By the way, we keep ALL of our parking permits from our dashboard (and, yes, they get you free parking at all parks and resorts). In fact, we keep the last one there all the way until our next trip as inspiration on those days that driving to work is just painful.